Engineering Economics - Flashcard set - Civil Engineering

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Future Worth Analysis

Future Worth Analysis finds the value of a present cash flow at a future date, accounting for interest or growth over time. Example Calculation:

FW = P(1+r)^n

where

FW

is the future worth,

P

is the present value,

n

is the number of periods, and

r

is the interest rate.

Break-Even Analysis

Break-Even Analysis determines the point at which revenue equals costs, resulting in no net loss or gain. Example Calculation:

\text{Break-Even Point (Units)} = \frac{\text{Fixed Costs}}{\text{Price per Unit} - \text{Variable Cost per Unit}}

Sunk Cost

A sunk cost is a cost that has already been incurred and cannot be recovered. Example: Costs spent on research that did not lead to a viable product.

Internal Rate of Return (IRR)

IRR is the discount rate that makes the net present value of all cash flows (both positive and negative) from a particular project equal to zero. Example Calculation:

0 = \sum_{t=0}^{n} \frac{C_t}{(1+IRR)^t}

Solve for the IRR where

C_t

is the cash flow at time

t

and

n

is the number of periods.

Depreciation (Straight-Line Method)

Straight-Line Depreciation is a method where the asset's cost is reduced uniformly over its useful life. Example Calculation:

\text{Annual Depreciation} = \frac{\text{Initial Cost} - \text{Salvage Value}}{\text{Useful Life}}

Opportunity Cost

Opportunity Cost is the value of the next best alternative forgone as the result of making a decision. Example: The cost of studying for an extra hour could be the leisure time sacrificed.

Present Worth Analysis

Present Worth Analysis discounts future cash flows to the present to compare different projects. Example Calculation:

PW = \sum_{t=0}^{n} \frac{C_t}{(1+r)^t}

where

PW

is the present worth,

C_t

the cash flow at time

t

,

n

is the number of periods, and

r

is the discount rate.

Annual Worth Analysis

Annual Worth Analysis converts cash flows of different amounts occurring over different times into a uniform annual series of cash flows. Example Calculation:

AW = \frac{PW}{AF}

where

AW

is the annual worth,

PW

is the present worth, and

AF

is the annualizing factor.

Life Cycle Cost Analysis (LCCA)

LCCA is the total cost of ownership over the life of an asset. Example Calculation:

LCCA = C_{initial} + \sum_{t=1}^{n} \frac{C_t}{(1+r)^t}

where

C_{initial}

is the initial cost,

C_t

is the cost at year

t

,

n

is the life of the project, and

r

is the discount rate.

Economies of Scale

Economies of Scale occur when a company's production costs decrease as it produces more units. Example: A company may receive a discount on bulk orders of raw materials.

Risk Analysis

Risk Analysis involves quantifying the probabilities and consequences of risks. Example: Calculating the potential overruns in cost or time for construction projects.

Sensitivity Analysis

Sensitivity Analysis is used to understand how different values of an independent variable affect a particular dependent variable. Example: Assessing how changes in interest rates affect the outcome of a project investment.

Net Present Value (NPV)

NPV is the value of a series of cash flows over time, brought to the present. Example Calculation:

NPV = \sum_{t=0}^{n} \frac{C_t}{(1+r)^t}

where

C_t

is the cash flow at time

t

,

n

is the total number of periods, and

r

is the discount rate.

Marginal Cost

Marginal Cost is the change in total cost that arises when the quantity produced changes by one unit. Example Calculation:

\text{Marginal Cost} = \frac{\Delta C}{\Delta Q}

where

\Delta C

is the change in costs and

\Delta Q

is the change in quantity.

Discount Rate

The discount rate is the rate used to convert future economic value into present value. Example Calculation:

PV = \frac{FV}{(1+r)^n}

where

PV

is the present value,

FV

is the future value,

n

is the number of years, and

r

is the discount rate.

Cost Performance Index (CPI)

CPI measures the financial effectiveness of project activities by comparing the budgeted cost of work performed with the actual cost. Example Calculation:

CPI = \frac{EV}{AC}

where

EV

is the earned value and

AC

is the actual cost of work performed.

Payback Period

The Payback Period is the time it takes for the cash inflows to repay the initial investment. Example Calculation:

\text{Payback Period} = \frac{\text{Initial Investment}}{\text{Annual Cash Inflow}}

Escalation

Escalation refers to the provision in cost estimate for inflation or cost increases over time. Example: A construction project may factor in a 4% annual escalation in material costs due to inflation.

Benefit-Cost Ratio (BCR)

BCR is a ratio that compares the benefits of a project to its costs. Example Calculation:

BCR = \frac{\sum_{t=0}^{n} \frac{B_t}{(1+r)^t}}{\sum_{t=0}^{n} \frac{C_t}{(1+r)^t}}

where

B_t

is the benefit at time

t

,

C_t

are costs at time

t

,

n

is the total number of periods, and

r

is the discount rate.

Return on Investment (ROI)

ROI is a measure of the profitability and efficiency of an investment. Example Calculation:

ROI = \frac{\text{Net Profit}}{\text{Investment Cost}} \times 100\%

where Net Profit is the gain from investment minus the cost of investment.

Inflation and Deflation

Inflation is the rate at which the general level of prices for goods and services is rising, and subsequently, purchasing power is falling. Deflation is the decrease of the general price level. Example: If annual inflation rate is 3%, a $100 product will cost$ 103 next year.

Externalities

Externalities are costs or benefits incurred by third parties outside the transaction without compensation. Example: Pollution from a plant can affect the health of nearby residents without the plant incurring costs ('negative externality').

Schedule Performance Index (SPI)

SPI is a measure of schedule efficiency which is used to predict the project duration. Example Calculation:

SPI = \frac{EV}{PV}

where

EV

is the Earned Value and

PV

is the Planned Value.

Engineering Economic Decision Matrix

This matrix is a tool used to compare multiple projects or design alternatives based on several criteria (e.g., NPV, IRR, payback period). Example: A matrix comparing different engineering solutions for their expected costs, benefits, and economic payback times.

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